Civ Design 4

7/21/2019 Civ Design 4

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Summary

Two post-tensioned beams made out of Styrofoam, rubber bands and match

sticks were investigated when specic loads were placed at the mid-span.The main purpose of this report was to obtain the engineering characteristics

of post-tensioned beams using scaled models. The beam when loaded is

supposed to show similar characteristics to that of a simply supported beam.

Each beam contains the same material, but when constructed the rubber

band, which represent the neutral axis was placed at dierent locations. The

beam whose neutral axis is located !mm from the base is initially hogging,

and when a load is placed the beam neutrali"es and it begins to sag as load

is increased. The beam with the neutral axis through the centre behaves

similarly except when constructed it was at a neutral position, rather than

hogging.

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1.0 Introduction

#ost-tensioning is a method of producing prestressed concrete, masonry and

other structural elements. The term pre-stressing is used to describe the process ofintroducing internal forces $or stress% into a concrete or masonry element during the

construction process in order to counteract the external loads that aect the

structure when it is in use $service loads%. &n post-tensioning, high-strength steel

strands or bars coated with a protective coating and housed in a duct or sheathing

are used to reinforce the concrete. These are typically called tendons.

There are various advantages of utili"ing prestressed concrete as it possesses

great strength and overcomes concrete's natural weakness in tension. &t is used to

produce beams, bridges or (oors with a longer span than is practical with ordinary

reinforced concrete.

The rst recorded use of post tensioning is in )*++ by Eugene reyssinet, for the

foundation of a marine terminal in rance. The techniue was then used in the S/

in the )*01's for the 2alnut 3ane 4ridge in #hiladelphia. &t is now used extensively

in bridges, elevated slabs and other various structures.

#ost tensioning in buildings can be divided into two dierent categories. 5ne

application is for speciali"ed structural elements, including transfer beams and

plates, raft foundations, tie-beams etc. The other application is building (oor

systems.

&n this experiment, a model system of post-tensioned beams was constructedusing styrotex cubes and rubber bands. &t was then loaded with coins to test the

strength of the structure and ualitative and uantitative analysis on the system

was conducted on the observations. The results were then used to describe the

operation of post-tensioned beams.

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2.0 Background Information

6.) 4ending of 4eams

2hen a beam experiences a bending moment it will change its shape and internal

stresses will be developed. 4ending in a beam produces either hogging or sagging.

7ogging and sagging describe the shape of a beam or similar long ob8ect when

loading is applied. 7ogging describes a beam which curves upwards in the middle,

and sagging describes a beam which curves downwards. &n a post-tensioned beam

it is expected that it will initially hog then as loads are added, it will move from that

position to a neutral one, then one of sagging.

The lower the neutral axis and the centre of gravity, the better the beam is

expected to behave under a tensional stresses. Thus as the load is increase on the

beam, it is expected that the beam with the lower neutral axis will be more sturdy

and would fail at a higher load than a beam with the neutral axis in the centre or

higher from the base.

&n this experiment it will investigate the dierence between two post-tensioned

beams. 5ne where the compressive forces are applied to the center of beam and

the other where the compressive force is applied )1 mm from the base of the beam.

Uses of post-tensioned beams

/s stated in the introduction, concrete is very strong in compression but weak in

tension, therefore it will crack when forces act to pull it apart. &n conventional

concrete construction, if a load such as a truck is applied to a beam, the beam will

tend to de(ect or sag causing the bottom of the beam to elongate slightly which

then leads to cracking.

Steel reinforcing bars $9rebar:% are typically embedded in the concrete as tensile

reinforcement to limit the crack widths and are called passive reinforcement

however, it does not carry any force until the concrete has already de(ected enoughto crack. #ost-tensioning tendons are considered active reinforcing since it is

pretested and the steel is eective as reinforcement even though the concrete may

not be cracked.

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3.0 Adantages of Using !ost-"ensioned Beams

#ost-tensioned beams are advantageous as opposed to regular reinforced

concrete beams due to its ability to overcome concrete's natural weakness in

tension. /rchitects, engineers and contractors incorporate post-tensioning systems

in their works for e


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A!!A$A"US A%& 'A"($IA)S

G +1x+1x+1mm Styrofoam cubes

G @ubber bands

G @oller support $Hork%

G ixed support $styrofoam cube%

G @uler

G 60 cent coins

G Iatchsticks

4E/I )

@44E@ 4/J /T HEJTE@

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!$+,(&U$(=

). Eight Styrofoam cubes which measured +1mm long, +1mm wide and

+1mm

6. / point, located at the center o each cube and the rubber band was

then threaded through each.

+. Iatch sticks were used to anchor the rubber band on either side of the

beam.

C. / second beam was fabricated. 7owever, the rubber band was strung

at a distance of )1mm from the base of each cube.

0. The rst beam was placed on a roller support $bottle cork% and a xed

support $wooden block%

A. The distance from the base of the beam to the desk $datum level% was

measured and recorded as, uK

B. Hoins were then placed on the beam in increments of 6 until a failure

point was reached.

!. /fter each increment of coins was added the distance from the base to

the datum level was measured $u'%

*. The de(ection, u was then calculated $uLuK-u'%

)1. Steps 0-* were repeated using the second beam.

)). The results were tabulated.

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$esuts

#ost Tensioned 4eam ) M )0 mm

from base

2eight of each coin L +.0 g L

1.1+0 J

nloaded 7eight above the atum

$u'1% L 6) mm

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%umber of,oins

eigt g

eigt %

u4mm

umm

1 1 1 6) 16 B 1.1B 61 )C )C 1.)C )*.0 ).0

A 6) 1.6) )* 6! 6! 1.6! )!.B 6.+

)1 +0 1.+0 )!.6 6.!)6 C6 1.C6 )B.! +.6)C C* 1.C* )B.+ +.B)A 0A 1.0A )A.* C.))! A+ 1.A+ )A 061 B1 1.B )C.0 A.066 BB 1.BB )6 *6C !C 1.!C ! )+

6A *) 1.*) 0 )A6! *! 1.*! 1 6)

"abe 15 )oad 6s &e7ection 8or !ost "ensioned Beam 1

1 1.6 1.C 1.A 1.! ) ).6

1

0

)1

)0

61

60

)oad 6s &e7ection

3oad Ns e(ection

,art 15 )oad s &e7ection for %orma Beam

#ost Tensioned 4eam 6 -)1mm

from base

2eight of each coin L +.0 g L

1.1+0 J

nloaded 7eight above the atum

$u'1% L +C mm

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%umberof ,oins

eigt g

eigt%

u4mm

umm

1 1 1 +C 16 B 1.1B +C 1

C )C 1.)C +C 1A 6) 1.6) +C 1! 6! 1.6! ++ )

)1 +0 1.+0 ++ ))6 C6 1.C6 ++ ))C C* 1.C* ++ ))A 0A 1.0A +6.0 ).0)! A+ 1.A+ +6.0 ).061 B1 1.B +6 666 BB 1.BB +).0 6.0

6C !C 1.!C +) +6A *) 1.*) +1.0 +.06! *! 1.*! +1 C+1 )10 ).10 6! A+6 ))6 ).)6 6B B+C ))* ).)* 6A !+A )6A ).6A 6C.0 *.0+! )++ ).++ 6) )+C1 )C1 ).C )B )BC6 )CB ).CB )C 61

CC )0C ).0C )) 6+"abe 25 )oad s &e7ection for !ost "ensioned Beam

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1 1.6 1.C 1.A 1.! ) ).6 ).C ).A ).!1

0

)1

)0

61

60

3oad Ns e(ection -#ost-tensioned 4eam

3oad $J%

e(ection $mm%

&iscussions

Thisexperiment uses Styrofoam and elastic bands to model post-tensioned

beams.

The rst beam was designed with the pre-stressed reinforcement $elastic

band% running along the center of the beam.

This beam began to de(ect as soon as load was applied. rom Hhart ) it was

shown to have yielded at )A coins and totally collapsed at 6! coins.

The second beam was designed with the reinforcement )1mm from the base

of the beam. The results from this conguration were very dierent.

&t was seen that the post-tensioned held a much greater load than the

unstressed beam. The post tension beam as shown in Hhart 6 yielded at +1

coins and totally collapsed at CC coins.

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igure )= showing set up of beam 6

The beam was noticeably tenser than the rst beam upon handling, and the

top of the beam was undergoing tension while the bottom was undergoingcompression. This is mainly because the Styrofoam cubes had be 8oined

)1mm from the bottom. 4efore loading the height at the center was greater

than the height at the supports. . pon loading there was no change in the

vertical height for several applications. Took 6! coins $*! grams% for the

beam to be parallel to the table. Eventually the beam began to deform, but

the rate of deformation began slowly and started to increase rapidly after it

yeilded. Then the beam nally failed at an application of CC coins.

igure A= showing failure of beam 6

This experiment shows us that that beam 6 is the stronger beam because by

applying the resulting compressive force to a point other than the centroid, it

not only resists the tensile forces in the block but &t also creates a hogging

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bending moment in the beam to counteract the sagging moment caused by

the applied loads.

)imitations

G #arallax, measurements were taken at eye level

G Extract force was added when the coins were loaded because there

couldn't be loaded steady for accuracy

G The holes of the cubes were not at the exact same position.

G #lacing the coins singly would have been a more accurate approach

than loading in two's $6%.

G The coins were not stacked straight, there was a slight deviation to one

side, which at times resulted in toppling of coins.

$ecommendations

G se a completely (at surface when testing the model.

G Ensure that the supports are the exact same height from the surface tothe beam

G Ensure the coins are stacked straight and exactly at the centre of the

beam.

G Take more than one set of readings and nd the average of the values

to reduce errors and increase accuracy of the data.

G Stack the coins in smaller intervals.

G Ensure that the holes are punched at the exact same position for eachcube.

G se new rubber bands to ensure a high degree of elasticity.

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,oncusion

/lthough pre-stressing all beams would add strength to the beam. The beam

can be made stronger by shifting the pre-stressed 9tendons: away from the

centroid in order to create a counteractive bending moment to counter the

moments applied when the beam is loaded. This was tested and proven in

beam 6.

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$eferences

http=DDwww.builderspt.comDwp-

contentDthemesDbuilderposttensionDbasicOpostOtension.pdf

http=DDwww.amsyscoinc.comDproducts-servicesDencapsulated-post-tensionDbenets-

of-post-tensioningD

http=DDwww.stresscrete.co.n"DeducDfprestress.html

http=DDwww.shaymurtagh.co.ukDproductsDconcrete-bridge-beamsD

http=DDen.wikipedia.orgDwikiD#restressedOconcrete

http=DDwww.childs-ceng.demon.co.ukDtutorialDtuCC.html

1# | # a g e
http://www.amsyscoinc.com/products-services/encapsulated-post-tension/benefits-of-post-tensioning/http://www.amsyscoinc.com/products-services/encapsulated-post-tension/benefits-of-post-tensioning/http://www.stresscrete.co.nz/educ/fprestress.htmlhttp://www.shaymurtagh.co.uk/products/concrete-bridge-beams/http://en.wikipedia.org/wiki/Prestressed_concretehttp://www.stresscrete.co.nz/educ/fprestress.htmlhttp://www.shaymurtagh.co.uk/products/concrete-bridge-beams/http://en.wikipedia.org/wiki/Prestressed_concretehttp://www.amsyscoinc.com/products-services/encapsulated-post-tension/benefits-of-post-tensioning/http://www.amsyscoinc.com/products-services/encapsulated-post-tension/benefits-of-post-tensioning/

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Civ Design 4